Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source

摘要

In this paper, the blow-up rate of solutions of semi-linear reaction-diffusion equations with a more complicated source term, which is a product of nonlocal (or localized) source and weight function a (x), is investigated. It is proved that the solutions have global blow-up, and that the rates of blow-up are uniform in all compact subsets of the domain. Furthermore, the blow-up rate of | u (t) |_∞ is precisely determined.